Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush lightly with olive oil, and roast for 15-20 minutes until tender.
While eggplant roasts, brown the ground lamb in a skillet over medium heat with diced onion and minced garlic until the meat is cooked through.
Stir in the tomato sauce, cinnamon, oregano, salt, and pepper, then simmer for 5 minutes to let the flavors meld.
In a small bowl, whisk together the Greek yogurt and the egg until smooth.
In a small baking dish, layer half of the roasted eggplant slices, top with the lamb mixture, and then the remaining eggplant.
Spread the yogurt and egg mixture evenly over the top and sprinkle with parmesan cheese.
Bake for 20-25 minutes until the topping is set and golden brown.